Can both arterial insufficiency and venous insufficiency cause a cold leg? how are the two distinguished?

No: Critical arterial insufficiency causes a cold, cyanotic, pulseless, painful leg. Venous insufficiency causes a swollen leg with dilated veins. The color can be normal or plethoric (reddish). If phlebitis is present, the leg may be painful, but uncomplicated venous insufficiency doesn't necessarily hurt. You mention knee swelling - do you have an effusion? If so, this is not vascular.